Well, technically, all batteries are removable, just always easily.
If the laptop is still under warranty, I would suggest contacting the manufacturer. If it isn't under warranty still, then try this.
Make sure the laptop is off, and try and charge the battery. Does it charge completely then? If yes, then try using another charger cord, when it is on, and see if it will charge the battery. If it still charges, then your cord is/was the problem.
Now if neither of those work, then it is probably the battery.